Question: Let ( = {(1, (2,...} and let A be a -field of subsets of (. Then show that (i) A = P(() if and only

Let ( = {(1, (2,...} and let A be a σ-field of subsets of (. Then show that
(i) A = P(() if and only if {(i} ( A for all (i.
(ii) A measure μ on A(=P (()) is determined by defining μ ({(i}), i ( 1.

Step by Step Solution

★★★★★

3.38 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

i If i A for all i then clearly every s... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

742-M-S-P (6798).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let V Î¸ be open in R2. A function F: V R2 is said to be conservative on V if and only if there is a function f : V R such that F = f on V. Let (x, y) V and let F = (P, Q) : V R2 be...

Let (1, (2 be two spaces and let A, Ai ( (1, B, Bi ( (2, i = 1, 2. Then show that. (i) (A1 B1) (A2 B2) = [(A1 ( A2] (B1 - B2) + [(A1 - A2)] B1]. (ii) A B = (, if and if at least one of A, B is...

Let A1,..... An be arbitrary subsets of an abstract set (, and let A'i be either Ai or Aci, i = 1,.... n. Define the class C of subsets of ( as follows: C = {all unions of the intersections A'1 (...(...

Let X be a finite set, let 1 , 2 , ... , A 1 ,A 2 ,...,A n be subsets of X, and let I be a subset of [ ] [n]. Show that the number of elements of X which belong to A i for all iI but for no other...

Let ( = {0, 1, 2,....}, let A be the discrete -field of subsets of (, and on A, define the function by: (A) = number of nonnegative integers in A. Then show that is a measure, and indeed, a -finite...

U ref use text name. for book search on google Show written solutions for all of the following problems. Unit 5: Counting Theory Text: A Spiral Workbook for Discrete Mathematics. 8.2: Addition and...

4. For any positive integer n let [n] = {1, 2, ...,n}. Let F be any collection of subsets of [n]. [10] A hitting set for F is any subset U C [n] such that for all S EF, UNS +). Consider the following...

(10 points) Construct a finite field of 16 elements as F2(a)/4 + 1. Show that is a primitive element in the field, and express every element of the field as a power Of . . Identify all the primitive...

3. (10 pts.) Let A be a set with at least two elements, and let a and b be two distinct elements of A. Define P, as the set consisting of all the subsets of that contain a, while P, is the set...

Please show all work to support your answer 1. Let = {, , , , 1, 2, 3,{4,5}} which of the following is true [careful]? A. {} B. C. 4 D. {1,2} 2. One of the following is a subset of =...

Under Armour reported the following in its 2018 Form 10-K. Under Armour's income statement reported 2018 cost of goods sold of $2,852,714 thousand. Its balance sheet reported inventories of $917,546...

Express the periodic function shown below as a Fourier Series Expansion. Simplify to lowest terms. 1 4 -3 -1

A company that rents campervans in New Zealand is checking whether the number of days campervans are rented is lower in the South Island than in the North Island. Campervans from this company are not...

Do global products exist, or is it global brands which exist? Make a list of global products, services or brands. How can they be categorized? Does this categorization help you to decide what it is...

Each of three machined parts is classified as either above or below the target specification for the part.

Each of four transmitted bits is classified as either in error or not in error.

In the final inspection of electronic power supplies, three types of nonconformities might occur: functional, minor, or cosmetic. Power supplies that are defective are further classified as to type...

Which EAP method requires installing digital certificates on both the server and client? PEAP EAP - CA EAP - TLS EAP - SSL

Read the quotes from to the article: The Bank of Russia took steps on Monday to restore confidence, and more than doubled interest rates to 20 percent from 9.5 percent in order to offset the rapid...

Blue Bull, Inc., has a target debt-equity ratio of .77. Its WACC is 8.6 percent, and the tax rate is 30 percent. Required: (a) If the companys cost of equity is 11.7 percent, what is its pretax cost...